plugin-Math255-Pset11 - Winter 2010 Math 255 Problem Set 11...

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Winter 2010 Math 255 Problem Set 11 Due Tuesday 30 March Section 16.7: 16, 26, 40, 44 Section 16.8: 6, 14, 26, 38 Section 16.9: 6, 8, 16, 24 Challenge Problems : ai) Let f = r α , where r 2 = x 2 + y 2 or r 2 = x 2 + y 2 + z 2 . Recall the definition of an improper integral. For what α does: 1. R R U f d A exist when U = { ( x, y ) | x 2 + y 2 1. 2. R R U f d A exist when U = { ( x, y ) | x 2 + y 2 1. 3. R R R U f d V exist when U = { ( x, y, z ) | x 2 + y 2 + z 2 1. 4. R R R U f d V exist when U = { ( x, y, z ) | x 2 + y 2 + z 2 1. aii) Discuss your results in light of Fubini’s theorem (be sure to state the version of Fubini’s theorem you refer to and where you found it). b) Suppose that R R R U f d V = 0 for all regions U R 3 . Suppose f is continuous. Explain why f = 0. c) A class is graded on a curve. It is assumed that the class is a representative sample of the population, the probability density function for the numerical score x is 1
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Winter 2010 Math 255 given by f ( x ) = C exp ( x - μ ) 2 2 σ 2 . For simplicity we assume that x can take on the values -∞ and , though in actual fact the exam is scored from 0 to 100.
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